This paper presents an efficient methodology for discrete Asian options that is consistent with different types of underlying densities – especially non-normal returns as suggested in the empirical literature (Mandelbrot, 1963, and Fama, 1965). The interest of this method is its greater flexibility than more standard methods. Based on a fast Fourier transform technique, the method is an enhanced version of the algorithm of Carverhill and Clewlow (1992). The contribution of this paper is to improve their algorithm and to adapt it to non-lognormal densities. This enables us to examine the effect of fat-tailed distributions on price as well as on delta. We find evidence that fat tails lead to larger jumps in the delta.